N. Nirmalkar

Forced Convection from a Heated Equilateral Triangular Cylinder in Bingham Plastic Fluids

The momentum and forced convection heat transfer characteristics of a heated equilateral triangular cylinder immersed in a Bingham plastic fluid have been studied numerically. The governing equations (continuity, momentum, and thermal energy) are solved for both vertex-upstream and vertex-downstream orientations, over wide ranges of the pertinent parameters, such as Reynolds number: 0.1 ≤ Re ≤30; Prandtl number: 1 ≤ Pr ≤100; and Bingham number: 0 ≤ Bn ≤200. Over the range of conditions, the flow is expected to be steady and symmetric. Detailed analysis of the flow and heat transfer phenomena in the vicinity of the cylinder is performed by a thorough inspection of the streamline and isotherm contours. Furthermore, due to the presence of the yield stress, the flow domain consists of yielded (or fluid-like) and unyielded (or solid-like) zones. The effect of Reynolds number and Bingham number on the shape and size of these zones has been thoroughly examined in terms of the detailed velocity and shear rate profiles. At the next level, the functional dependence of the drag and Nusselt number on the Reynolds number, Bingham number, and Prandtl number is explored and developed. The heat transfer results spanning the above-noted ranges of parameters are consolidated by developing a correlation in terms of the Colburn j h factor as a function of the modified Reynolds number.

Mixed Convection from a Heated Sphere in Bingham Plastic Fluids

In this work, the steady and laminar mixed-convection heat transfer from an isothermal sphere immersed in Bingham plastic fluids has been investigated in the aiding-buoyancy configuration. The pertinent coupled equations of motion and thermal energy have been solved numerically over the following ranges of conditions: Richardson number, 0 ≤ Ri ≤ 2, Bingham number, 0 ≤ Bn ≤ 10, Reynolds number, 0.1 ≤ Re ≤ 100 and Prandtl number, 10 ≤ Pr ≤ 100. Flow characteristics like streamlines, pressure coefficient, morphology of yielded/unyielded regions and drag coefficient are discussed extensively. Similarly, isotherms, local Nusselt number and average Nusselt number are thoroughly examined to develop an overall understanding of the corresponding heat transfer characteristics. All else being equal, in contrast to the positive role of the aiding-buoyancy free convection in Newtonian and power-law fluids, due to the fluid yield stress, heat transfer is impeded in viscoplastic fluids. While the average value of the Nusselt number is influenced by four dimensionless groups, namely, Reynolds number, Bingham number, Prandtl number and Richardson number, by using novel scaling, it has been possible to consolidate the present results via the use of the Colburn j-factor in a simple form. This is particularly suitable for predicting the value of the Nusselt number in a new application.

Effect of confinement on forced convection from a heated sphere in Bingham plastic fluids

In this work, the momentum and heat transfer characteristics of a heated sphere in tubes filled with Bingham plastic fluids have been studied. The governing differential equations (continuity, momentum and thermal energy) have been solved numerically over wide ranges of conditions as: Reynolds number, 1 ≤ Re ≤ 100; Prandtl number, 1 ≤ Pr ≤ 100; Bingham number, 0 ≤ Bn ≤ 100 and blockage ratio,0 ≤ λ ≤ 0.5 where λ is defined as the ratio of the sphere to tube diameter. Over this range of conditions, the flow is expected to be axisymmetric and steady. The detailed flow and temperature fields in the vicinity of the surface of the sphere are examined in terms of the streamline and isotherm contours respectively. Further insights are developed in terms of the distribution of the local Nusselt number along the surface of the sphere together with their average values in terms of mean Nusselt number. Finally, the wall effects on drag are present only when the fluid-like region intersects with the boundary wall. However, heat transfer is always influenced by the wall effects. Also, the flow domain is mapped in terms of the yielded- (fluid-like) and unyielded (solid-like) sub-regions. The fluid inertia tends to promote yielding whereas the yield stress counters it. Furthermore, the introduction of even a small degree of yield stress imparts stability to the flow and therefore, the flow remains attached to the surface of the sphere up to much higher values of the Reynolds number than that in Newtonian fluids. The paper is concluded by developing predictive correlations for drag and Nusselt number.

Effect of Orientation on Mixed Convection from a Heated Square Bar in Newtonian and Power-Law Fluids

In this work, mixed convective heat transfer from a heated square bar at an incidence of 45° in power-law fluids has been investigated numerically in the so-called aiding buoyancy configuration. The governing differential equations have been solved over the following ranges of conditions: Richardson number, 0 ≤ Ri ≤ 2, power-law index, 0.2 ≤ n ≤ 1, Reynolds number, 1 ≤ Re ≤ 40, and Prandtl number, 0.7 ≤ Pr ≤ 100. The detailed flow and heat transfer characteristics have been visualized in terms of the streamline and isotherm contours adjacent to the surface of the heated cylinder. The macroscopic heat and momentum transfer characteristics, like local and average values of the Nusselt number (Nu) and drag coefficients (CD), have been analyzed as functions of the Reynolds number (Re), Prandtl number (Pr), Richardson number (Ri), and power-law index (n). Further insights are provided in terms of the distribution of the pressure coefficient and local Nusselt number along the surface of the tilted square. As expected, the value of the local Nusselt number decreases from its maximum value at the front stagnation point along the surface of the bar. Over the range of conditions spanned here, the flow is steady and symmetric about the vertical centerline. Finally, the present numerical values of the average Nusselt number are correlated using a nonlinear regression approach which facilitates interpolation of the present results for the intermediate values of the governing parameters.